How did a stranger send me a message on Facebook?

I noticed yesterday that I had a message in my “other” message inbox. It was from a total stranger and said something like “Hello Gorgeous, I’d like to get to know you if that’s alright. Cheers!” It was (purportedly) from some guy in the UK. I’m not searchable in Facebook by name to begin with and my privacy settings are set so that only friends of friends can contact me. This guy is not a friend of a friend. So, can anyone tell me how this guy was able to contact me and, since he commented on my looks, how he saw my profile photo? It’s so weird. I’ve gone back and forth in the Facebook privacy settings and confirmed all my settings are correct, but I can no longer see any option boxes about who can send you messages. I don’t get how he could have found me to message me in the first place.